Scaling behavior in economics: II. Modeling of company growth

Sergey V. Buldyrev, Luís A Nunes Amaral, Shlomo Havlin, Heiko Leschhorn, Philipp Maass, Michael A. Salinger, H. Eugene Stanley*, Michael H R Stanley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


In the preceding paper [1] we presented empirical results describing the growth of publicly-traded-United States manufacturing firms within the years 1974-1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an "optimal" size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent β, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that β= - In Π/ In z, where z defines the mean branching ratio of the hierarchical tree and Π is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.

Original languageEnglish (US)
Pages (from-to)635-650
Number of pages16
JournalJournal de Physique II
Issue number4
StatePublished - Dec 1 1997

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • General Engineering
  • Physics and Astronomy (miscellaneous)


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